## The number of replications.
nrep = 1e4

## The sample size from each instrument.
n = 10

## The mean value of the bad data.
mu2 = 0.5

## A grid of proportions to consider.
Q = seq(0, 1, 0.1)

V = array(0, c(length(Q),4))

## Check each prortion in Q to see how it performs.
for (k in 1:length(Q)) {

    ## The good data.
    X1 = rnorm(nrep*n)
    X1 = array(X1, c(nrep,n))
    M1 = apply(X1, 1, mean)

    ## The bad data.
    X2 = rnorm(nrep*n, mean=mu2)
    X2 = array(X2, c(nrep,n))
    M2 = apply(X2, 1, mean)

    ## The estimator.
    M = Q[k]*M1 + (1-Q[k])*M2

    ## Estimate bias, variance, and MSE from the simulation.
    bias = mean(M)
    variance = var(M)
    mse = mean(M^2)

    V[k,] = c(bias, variance, bias^2+variance, mse)
}